Question

What is the graph of the absolute value equation?

y = |x + 3| – 4

Answer 1

try to substitute values and draw a graph

Answer 2

think of the absolute values as parenthesis

if you subtract 4 outside the parenthesis, what do you do to the graph?

Answer 3

go down cuz its negative right?

Answer 4

brb

Answer 5

right, the graph will be shifted downwards by 4 units

Answer 6

so which 2 graphs look like they have been shifted downwards by 4 units?

Answer 7

one and two

Answer 8

good, now we look at inside the parenthesis

if we add 3 inside the parenthesis, what do we do to the graph?

Answer 9

its capture 2

Answer 10

right?

Answer 11

nope

Answer 12

isnt that it cuz its positive?

Answer 13

lets look at the vertex of capture 2 (3,-4)

x=3

so if we subsitute in x=3 for y = |x + 3| – 4
we will get y=2
(3,2) is not the same as (3,-4) which is why capture 2 is incorrect

Answer 14

oh ok so it would be capture 1 cuz thats our only option left

Answer 15

its better to look at it like (x-a)
where a is the amount of units being shifted

a is positive when being shifted to the right, so it will look like (x-a)
if a is negative, when being shifted to the left, it will look like (x+a)

so its being shifted to the left 3 units

Answer 16

another way to think of it, is if look at the stuff inside the parenthesis, what number do i need to plug in, in order to get 0

in this case it would be -3, which means that -3 must be the vertex, or -3 is the amount i need to shift by

Answer 17

ok so Capture 1 is the final answer

Answer 18

yes, you can just plug in the vertex into the equation to see if it works

(-3,-4)

Answer 19

ok got it thank you sooo much!!! can you help me with one last question??